Shradha Mishra

Fluctuations and Pattern Formation in Self-Propelled Particles

We consider a coarse-grained description of a collection of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low-density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize both regimes.

Active Nematics Are Intrinsically Phase Separated

Two-dimensional nonequilibrium nematic steady states, as found in agitated granular-rod monolayers or films of orientable amoeboid cells, were predicted [Europhys. Lett. 62, 196 (2003)10.1209/epl/i2003-00346-7] to have giant number fluctuations, with the standard deviation proportional to the mean. We show numerically that the steady state of such systems is macroscopically phase separated, yet dominated by fluctuations, as in the Das-Barma model [Phys. Rev. Lett. 85, 1602 (2000)10.1103/PhysRevLett.85.1602]. We suggest experimental tests of our findings in granular and living-cell systems.

Collective dynamics of self-propelled particles with variable speed

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the specific variable speed rule used does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics.

Entanglement model of antibody viscosity.

Antibody solutions are typically much more viscous than solutions of globular proteins at equivalent volume fraction. Here we propose that this is due to molecular entanglements that are caused by the elongated shape and intrinsic flexibility of antibody molecules. We present a simple theory in which the antibodies are modeled as linear polymers that can grow via reversible bonds between the antigen binding domains. This mechanism explains the observation that relatively subtle changes to the interparticle interaction can lead to large changes in the viscosity. The theory explains the presence of distinct power law regimes in the concentration dependence of the viscosity as well as the correlation between the viscosity and the charge on the variable domain in our antistreptavidin IgG1 model system.

A dynamic renormalization group study of active nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally irrelevant. We discover a special limit of parameters in which the equation of motion for the angle field bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterparts.

Aspects of the density field in an active nematic

Active nematics are conceptually the simplest orientationally ordered phase of self-driven particles, but have proved to be a perennial source of surprises. We show here through numerical solution of coarse-grained equations for the order parameter and density that the growth of the active nematic phase from the isotropic phase is necessarily accompanied by a clumping of the density. The growth kinetics of the density domains is shown to be faster than the law expected for variables governed by a conservation law. Other results presented include the suppression of density fluctuations in the stationary ordered nematic by the imposition of an orienting field. We close by posing some open questions.

Topological-distance-dependent transition in flocks with binary interactions.

We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the nth topological neighbor; the specific value of n being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for n = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period t(c), then switches over to the ordered state and remains in this state ever after. For n = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for n≥3. Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase n. The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of n, which match well with their simulated values.

Giant number fluctuation in the collection of active apolar particles: from spheres to long rods

We study a collection of self-propelled apolar particles of different asymmetry on a two-dimensional substrate. Particle asymmetry is defined by different hopping probabilities along the long and short axes of the particle. Hopping probabilities p or s = 2p − 1 are introduced in such a way that p = 1/2 or s = 0.0 are spherically symmetric particles and p = 1 or s = 1.0 are elongated rod type particles. Number fluctuation for different hopping probabilities p is calculated analytically. Number fluctuation changes with the equilibrium limit for s = 0.0 to far from the equilibrium limit ΔN Na, a > 0.5 for non zero s. We calculate the density structure factor and number fluctuation numerically by solving nonlinear partial differential equations of motion for density and nematic order parameters. For small wave vector q, the structure factor diverges as and the corresponding number fluctuation for nonzero s.

Collection of polar self-propelled particles with a modified alignment interaction

We study the disorder-to-order transition in a collection of polar self-propelled particles interacting through a distance dependent alignment interaction. Strength of the interaction,

Phase separation in binary mixtures of active and passive particles

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